In a water pistol, a piston drives water through a larger tube of radius 1.17 cm

Question

In a water pistol, a piston drives water through a larger tube of radius 1.17 cm into a smaller tube of radius 1.36 mm as in the figure below.

(a) If the pistol is fired horizontally at a height of 1.11 m, use ballistics to determine the time it takes water to travel from the nozzle to the ground. (Neglect air resistance and assume atmospheric pressure is 1.00 atm. Assume up is the positive y-direction.)

(b) If the range of the stream is to be 8.22 m, with what speed must the stream leave the nozzle? (Assume the stream is traveling in the positive x-direction.)

(c) Given the areas of the nozzle and cylinder, use the equation of continuity to calculate the speed at which the plunger must be moved.

(d) What is the pressure at the nozzle? (Give your answer to three decimal places.)

(e) Use Bernoulli's equation to find the pressure needed in the larger cylinder.

(f) Calculate the force that must be exerted on the trigger to achieve the desired range. (The force that must be exerted is due to pressure over and above atmospheric pressure.)

Explanation / Answer

a) we can use y=y0+v0 t + 1/2 a t2

so 0=1.11+0.5(-9.81)t2 so t=0.476s

b) now use equation for x direction

8.22=0+v (0.476)+0 so v=17.269 m/s

c) using flow rate equation Av=Av

so v r2=vr2

v (1.17/100)2= 17.269 * (1.36/1000)2

so v =0.2333 m/s

d) 1 atm = 101000 Pa

e) Use Bernoulli's equation

101000+0.5*1000*17.2692=P+0.5*1000*0.23332

P=250082

f) F=P diff * A=(250082-101000)* (1.17/100)2=64.11 N

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